#### Explain solution RD Sharma class 12 chapter 7 Solution of Simultaneous Linear Equation Exercise Fill in the blank Question 1 Maths Textbook Solution.

Answer $\rightarrow x=1, y=-1, z=0$

Hint $\rightarrow I A=A$

Given

$\rightarrow\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 1 \\ -1 \\ 0 \end{array}\right]$

Explanation

$\rightarrow\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 1 \\ -1 \\ 0 \end{array}\right]$

$\left[\begin{array}{c} x \times 1+0 \times y+0 \times z \\ 0 \times x+1 \times y+0 \times z \\ 0 \times x+0 \times y+1 \times z \end{array}\right]=\left[\begin{array}{c} 1 \\ -1 \\ 0 \end{array}\right]$

$\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 1 \\ -1 \\ 0 \end{array}\right]$

Comparing both sides we get  $x=1,y=-1,z=0$